Question

If the error in the measurement of mass of a body is 3% and in the measurement of velocity be 2% .What will be the maximum possible error in calculation of kinetic energy?

Answer 1

Given :

• Percentage of error in measuring mass of body = 3%
• Percentage of error in measuring velocity of body = 2%

To Find :

• Maximum possible error in calculation of kinetic energy.

Solution :

$\implies{\sf \dfrac{\Delta m}{m}=3\% \: \implies \: 0.03}$

$\implies{\sf \dfrac{\Delta v}{v} = 2\% \: \implies \: 0.02}$

We know that ,

$\large\implies{\sf K = \dfrac{1}{2}mv^2 }$

K = Kinetic Energy

m = mass of body

v = Velocity of body

$\implies{\sf \dfrac{\Delta K}{K}=\dfrac{\Delta m}{m}+\dfrac{2 \Delta V}{V} }$

$\implies{\sf 0.03 + 2 \times 0.02}$

$\implies{\sf 0.03+ 0.04}$

$\implies{\sf 0.07 }$

$\implies{\sf \dfrac{\Delta K}{K}\times 100=0.07 \times 100 }$

$\implies{\bf \dfrac{\Delta K}{K}\%=7\%}$

Answer :

Maximum possible error in calculation of kinetic energy is 7%